Abstract
We consider a hierarchical pinning model introduced by B. Derrida, V. Hakim and J. Vannimenus in [3], which undergoes a localization/delocalization phase transition. This depends on a parameter B > 2, related to the geometry of the hierarchical lattice. We prove that the phase transition is of second order in presence of disorder. This implies that disorder smoothes the transition in the so-called relevant disorder case, i.e., \( B > B_c = 2 + \sqrt 2 \).
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© 2009 Birkhäuser Verlag Basel/Switzerland
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Lacoin, H., Toninelli, F.L. (2009). A Smoothing Inequality for Hierarchical Pinning Models. In: de Monvel, A.B., Bovier, A. (eds) Spin Glasses: Statics and Dynamics. Progress in Probability, vol 62. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9891-0_12
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DOI: https://doi.org/10.1007/978-3-7643-9891-0_12
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8999-4
Online ISBN: 978-3-7643-9891-0
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